Download SPECIAL ARTICLE The Continuum Model: An

Experimental Cell Research 185 (1989) 1-7
SPECIAL ARTICLE
The Continuum
Model: An Experimental
and Theoretical
Challenge to the Gl Model of Cell Cycle Regulation
ATSUYUKI
OKUDA*,’
and STEPHEN COOPER?
Virology, Medical Institute of Bioregulation, Kyushu University 69, Maidishi
*Department of
Fukuoka 812, Japan, and tDepartment of Microbiology and Immunology, University
of Michigan Medical School, Ann Arbor, Michigan 48109-0620
The dominant and current view of cell cycle regulation is that the controls for
cell proliferation reside primarily in the Gl phase of the division cycle. This
current or classical model is deeply ingrained in cell biology, and has been
described very well [ 1, 21; therefore we will only summarize below the basic
support of the Gl model. Over the past decade, however, an alternative proposal,
the continuum model, has emerged that suggests that there are no Gl-specific
events or controls, and that all of the evidence for the importance of the Gl phase
can be explained in terms of a continuous process that occurs in all phases of the
division cycle [3-71. These early reports addressed previous experimental results
and explained them in terms of the continuum model. In a sense, therefore, these
analyses were theoretical rather than experimental. The basic ideas of the continuum model are presented in Fig. 1.
Recently there has emerged a set of experiments that has been stimulated by
the ideas of the continuum model, and these experiments support the basic ideas
of the continuum model. This means that the continuum model has been a
stimulus to experimental tests, and therefore has an experimental as well as a
theoretical base. We will describe these experiments below, and explain how
they support the continuum model.
ANALYSIS OF THE Gl MODEL OF CELL CYCLE REGULATION
ACCORDING l-0 THE CONTINUUM MODEL
One may divide essentially all of the support for the Gl model of cell cycle
regulation into a number of groups or categories of experiments. These are:
Variability of GZ. The Gl phase of the cell cycle is the most variable. The
longer the Gl phase, the longer was the interdivision time of cells. This suggested
that the Gl phase regulates the rate of cell proliferation. The idea was that if cells
passed through the Gl phase very slowly, they would be slow-growing cells.
’ To whom reprint requests should be addressed.
1
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Okuda and Cooper
Gl
; G2
Time
Fig. 1. A schematic diagram of the continuum model. The lower sawtooth graph is the amount of
initiator per origin, varying from 0.5 to 1.0; a value of 1.0 is the critical amount required for the
initiation of DNA synthesis. At zero time the cells have just entered an S phase and the cells progress
through S and G2. The amount of initiator per origin increases from 0.5 to 1.0 over one interdivision
time (IDT). When the initiator per origin reaches 1.0 another S phase is initiated. Since there is a
sudden doubling in the number of available origins of replication the amount of initiator per origin
decreases immediately to 0.5. The concept of a doubling in “origins” is a formal concept, and in
reality there are many origins of replication in the eukaryotic S phase. The Gl period is the time
between the end of G2 and the start of S phase (here neglecting the short M period). If the rate of
initiator synthesis decreased and S and G2 remained constant, then Gl would increase. If the rate of
initiator synthesis increased, the Gl phase would decrease in length. As drawn in the upper graph, the
synthesis of initiator is continuous. No synthesis of particular regulatory molecules occurs in any
single phase of the division cycle.
GZ arrest. When cells are placed under nongrowth conditions, it is generally
found that cells are arrested with a GI content of DNA. This has been interpreted
as indicating that there is some point or event in the Gl phase of the division
cycle at which cells become arrested. The arrest point has sometimes been
referred to as the “restriction point”.
GZ euents. When ceils with a Gl amount of DNA are stimulated to resume
growth, a number of different proteins appear to be made specifically within the
Gl phase of the division cycle. This has been used to support the idea that there
are G 1-specific events.
G(O). The proposal of an out-of-cycle state, the G(O) phase, which a cell enters
from the GI phase of the division cycle, has supported the idea that the cell
makes proliferative choices in the Gl phase of the division cycle. This is one of
the Gl-specific events that are believed to occur in the Gl phase of the division
cycle. The importance of the G(O) phase is that it gives a general support to the
notion that there exist other Gl-specific events.
Cell cycle regulation
Gl
-GI
-Gl
- Gl
- Gl
s -
M -Gl
G2 -M
‘Gl
G2 -M
-Gl
s, -
Gl,==Gl,
M,--~-GI
Ga-M,-Gl,=Gl
Gq-MS-Gl,-Gl
Cessation of growth
Gl-arrest model
Gl =Gl
GI -Gl
Gl Gl
Gl -Gl
Continuum model
Gi, =
M
Gl GI”2
Gig S
-S
-S
S
4s
3
-G2
-M
-G2
-M
G2 M
-G2
-M
Gl,-Ss
Gl Gl, -SS
Gl;-GIM-Gl,
-Ss
Gl,Gl, -GIM-G1,-+Ss
Restart of growth
Fig. 2. Comparison of the Gl-arrest model of eukaryotic cell cycle regulation with the continuum
model. In the Gl-arrest model cells in all phases of the division cycle enter a resting phase with all
cells having a Gl content of DNA. This resting phase, signified by the italicized Gl, is entered from
the Gl phase of the division cycle. When cell growth restarts, cells leave this special state, sometimes
referred to as GO, and enter Gl. The cells then proceed through the division cycle. In contrast, the
continuum model proposes that there are two aspects that define the cycle phase of a cell. One is the
DNA content of a cell (signified by the large letters), and the other is the amount of initiator per origin,
indicated by the subscripts. When cells cease growing, the amount of initiator is held constant, and
the cells pass through the phases of the cycle so all cells have a Gl amount of DNA. When these cells
with a Gl amount of DNA are allowed to restart growth, the cells do not enter the division cycle all at
the same time. Rather, they enter the cycle in the order that they entered the resting phase. There is
no special unique state in which cells are resting. The cells have a Gl amount of DNA merely because
cells in S, or G2, or M phase must complete these phases and produce two Gl DNA-containing cells
even under deleterious conditions. There are no points in the Gl phase of the division cycle at which
cells come to rest.
Transition probability. The variability of cell cycle interdivision times has been
used to propose a model in which random transitions, generally associated with
the Gl phase of the division cycle, are the regulatory agents for cell cycle
proliferation. Although the transition probability model is quite different from the
Gl-event model, its proposal and wide acceptance as an alternative viewpoint
have lent added weight to the idea that the important, cell cycle regulatory phase
of the division cycle is the Gl phase.
The continuum model has reinterpreted these basic categories of support for a
Gl model of the division cycle. We will describe this alternative explanation, and
follow this with a description of the new experimental work that has been
presented to support the continuum model.
Variability of GZ. The continuum model proposes that the variable Gl is the
result of a variation in the times between initiations of DNA synthesis. The Gl
phase is what is left over when the time between initiations is greater than the time
for S, G2, and M [3]. The continuum model proposes that the observed variability of
Gl is a result of the variation in growth rate, rather than a cause of the
variation in growth rate. This is illustrated in Fig. 1. If S and G2 are constant, as
has generally been observed, then if the rate of initiator synthesis varies, large
changes in the Gl phase of the division cycle are produced. If cells grow very
rapidly, one can even eliminate the Gl phase of the division cycle [3]. This
elimination of the Gl phase is difficult to explain with the Gl-event model, but it
falls naturally out of the continuum model.
Gl arrest. The continuum model proposes that cells are arrested with a Gl
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Okuda and Cooper
amount of DNA merely because the deleterious conditions that are used to
produce nongrowing cells do not stop cells that are in the S, G2, or M phase of
the division cycle from proceeding to the completion of DNA synthesis and the
subsequent division [6]. The cells may have a Cl amount of DNA, but the
continuum model proposes that they are not “in Gl”. This is illustrated in Fig. 2,
where we see that the continuum model proposes that there is no special point or
event in Gl at which cells are arrested when they are placed under conditions that
do not support growth. The cells under a nongrowing condition have a Gl amount
of DNA because cells, in general, do not stop in S, G2, or M phase when
initiation of S phase is prevented. When growth is restarted, the cells are not
synchronized, but enter the S phase in the same order as that in which they
obtained a Gl DNA content during the inhibition of growth. The Gl model
proposes that there is a unique state, within the Gl phase, at which cells come to
rest. This is indicated by the italicized “Gl” in Fig. 2.
Gl events. The events that are generally proposed to be Gl events have
generally been found after stimulation of starved cells to resume growth. This
perturbation leads to various changes in the metabolism of the cell that make
various genes expressed at relatively high rates. Since the cells have a Gl amount
of DNA, this is interpreted as support for the existence of Gl events. The
continuum model suggests that these proposals are artifacts of the experimental
approach [6,7]. The continuum model suggests that the only reason that the cells
have a Gl amount of DNA is that they are difficult to arrest in the S, G2, and M
phases of the cycle. Thus, when cells are restarted, it only appears that the events
that are observed are Gl events. According to the continuum model it is only a
coincidence that cells with a Gl amount of DNA are the cells that are making a
particular set of biochemical changes during the restarting of growth.
G(O). The continuum model proposes that the G(0) phase is an artifact of the
prolonged starvation of cells under deleterious conditions [6, 71. The variable
conditions under which starved cells are found, and their variation in the resumption of normal growth, have been proposed to be an artifact of the starvation
conditions and no indication that there is a G(0) state. The G(0) state is illustrated
by the italicized “Gl” in the Gl model in Fig. 2.
Transition probability. The continuum model can account for and explain all of
the evidence for a transition probability regulating the cell cycle [S]. There is no
need to invoke a random mechanism for the regulation of the cell cycle. The
continuum model predictions fit all of the data better than the transition probability model [5], and in addition, explain the observed variability in terms of known
biochemical events [5].
NEW EXPERIMENTAL
SUPPORT FOR THE CONTINUUM
MODEL
The continuum model proposes that the regulation of the rate of cell cycle
progression, and the relative sizes of the various phases of the cell cycle, is due to
the rate of synthesis of mass or some specific subset of mass (the hypothetical
initiator) between the starts of S phases [3-71. One of the predictions of the
Cell cycle regulation
5
continuum model is that the failure to synthesize the requisite material in the
previous cycle will prolong the subsequent cell division. If this were found it
would mean that at division the start of a new set of events, occurring in Gl, was
not the regulatory process for cell division. Rather, this finding would mean that
there was a continuous process occurring during both the previous S and G2
phases and finishing in the subsequent Gl phase.
When rat 3Yl fibroblasts were deprived of serum in S or G2 phase, the cells
delayed entry into the S phase in the subsequent cycle [8, 91. The delay also
occurred when cells were prevented from adhering to the substrate [9] or were
exposed to caffeine [lo]. When the proliferating cells were deprived of serum [8]
or exposed to caffeine [lo] during Gl phase, they were inhibited from entering S
phase. The cells arrested with a Gl amount of DNA at confluent cell density were
also inhibited from entering S phase when incubated at a lower cell density under
each of the deleterious conditions [g-lo]. When cells expressing SV40 large T
antigen proceeded through S and G2 phases in the absence of serum, subsequent
entry into S phase was not markedly delayed after mitosis [ 111.The proliferating
cells expressing SV40 large T antigen, when deprived of serum in Gl phase,
entered S phase normally [ 111. The density-arrested cells entered S phase after
reseeding at a lower cell density with serum-free medium containing EGF, and
this effect was enhanced by addition of both insulin and transferrin [9]. The
effects of the growth factors paralleled the growth-factor-mediated shortening of
the delay in entry into S phase when the growth factors were added during the
serum deprivation period in the previous cycle [9]. Recent analysis of the
expression of c-fos and c-myc genes that were transiently and extensively induced in the cycling cells by change of culture condition from serum absence to
serum presence, or after cycloheximide addition, or after serum exposure to
density-arrested cells, has led to the proposal that the expression of these genes is
continuously required, in low amounts, in all phases of the cell cycle to allow
continued proliferation [12, 131. These results have been interpreted as support
for the continuous preparation for initiation of DNA synthesis occurring between
the starts of S phase, and thus are completely consistent with, and supportive of,
the continuum model.
Confirmation of these observations comes from time-lapse video analysis of
cell cycle interdivision times. The initial finding that cell division in low serum
proceeds normally for cells in the latter portion of the division cycle [14] was
originally interpreted as support for the G(0) phase of the cell cycle. But analysis
of the subsequent cycle revealed that the second mitosis, after a short treatment
in low serum, is delayed [15]. This has been shown to be completely in accord
with the predictions of the continuum model [16]. Recently the analysis of the cell
cycle of an alga [17] has lent additional and strong support to the continuum
model.
This brief analysis indicates that not only can the continuum model account for
all of the past results supporting the proposal of Gl-specific events, but the
predictions of the continuum model have been tested and found to be supported
by recent. experimental results. We suggest that the continuum model is an
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Okuda and Cooper
Continuum model
Gl -model
Fig. 3. The classical and continuum model icons for the eukaryotic division cycle. At the left is the
circular representation of the division cycle. At the right is the icon for the continuum model. The
main difference is that the continuum model proposes that termination of DNA replication and cell
division do not affect or regulate the subsequent initiation of DNA replication. The classical icon
implies that the end of each phase is the event that starts the next phase. This means that the end of M
phase starts a series of Gl events that eventually leads to the initiation of DNA synthesis or S phase.
In the continuum model cell division is the end of a process and the beginning of none.
important way to look at the division cycle, and that it allows a simplification of
cell cycle analysis. We hope that more workers would take a look at the utility of
the continuum model, and the various suggestions for its application [7].
The alternative ways of looking at the division cycle may be illustrated by
comparing the classical icon of the division cycle (Fig. 3, left) with the icon for
the continuum model (Fig. 3, right). The circular model of the division cycle
implies that the end of each particular phase initiates a new phase of the division
cycle. Thus, the end of the M phase starts a new Gl phase, and this Gl phase is a
phase with particular properties that can be investigated. The continuum model,
in contrast, sees the end of the S and G2 phases as the end of a process but this
ending does not start any new processes. Cell division does not initiate any new
series of events during the Gl phase that eventually lead to cell division. Preparations for division are continuous, as symbolized by the circle, and when S phase
starts a cell division follows after a sequence of S, G2, and M phases. Neither
termination of DNA synthesis nor the act of cell division regulates or alters the
continuous preparations for the initiation of DNA synthesis that is occurring in all
phases of the division cycle.
We hope that this presentation of the theoretical and experimental basis for the
continuum model leads to a reinterpretation of both past and future experimental
results in the light of this view of the division cycle. Although the great mass of
papers heretofore have interpreted their results from the classical viewpoint, we
feel that all of these results can be reinterpreted, reanalyzed, and shown to be
consistent with the predictions of the continuum model.
This work has been supported by National Science Foundation Grant DMB-8417403 to S.C.
REFERENCES
1. Baserga, R. (1985) The Biology of Cell Reproduction, Harvard Univ. Press, Cambridge, MA.
2. Baserga, R. (1976) Multiplication and Division in Mammalian Cells, Dekker, New York.
Cell cycle regulation
7
3. Cooper, S. (1979) Nature (London) 280, 17.
4. Cooper, S. (1981) Cell Biol. ht. Rep. 5, 639.
5. Cooper, S. (1982) J. Theor. Biol. 94, 783.
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159, 501.
Received April 17, 1989
Revised version received May 9, 1989
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